Polygonal · 2D · v1.0.0
Pentagon
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Mathematics
Geometric construction
Regular 5-gon inscribed in a circle of radius R; vertex k at angle 90° + 360°·k/5. Side length = 2R·sin(π/5).
Symmetry: Dihedral D5.
Culture
Symbolic interpretation
The pentagon's diagonals stand in the golden ratio to its sides — a mathematical fact; its symbolic readings are cultural.
Formulas
Available frequency mappings
- A · Direct ratio fᵢ = f₀ · rᵢ
- B · Power fᵢ = f₀ · rᵢ^α
- C · Logarithmic fᵢ = f₀ · 2^(k · log₂ rᵢ)
- D · Reference distance fᵢ = f₀ · (dᵢ / d_ref)^α
- E · Angular rᵢ = θᵢ / θ_ref ; fᵢ = f₀ · rᵢ^α
Units u
Coordinates
| id | x | y | z |
|---|---|---|---|
| P0 | 0.0000 | 0.0000 | 0.0000 |
| P1 | 0.0000 | 1.0000 | 0.0000 |
| P2 | -0.9511 | 0.3090 | 0.0000 |
| P3 | -0.5878 | -0.8090 | 0.0000 |
| P4 | 0.5878 | -0.8090 | 0.0000 |
| P5 | 0.9511 | 0.3090 | 0.0000 |
Distances & angles
|P1P2|1.1756 u
|P2P3|1.1756 u
|P3P4|1.1756 u
|P4P5|1.1756 u
|P5P1|1.1756 u
r(C0)1.0000 u
∠P2P1P51.8850 rad
∠P1P2P31.8850 rad
∠P2P3P41.8850 rad
∠P3P4P51.8850 rad
∠P4P5P11.8850 rad
Derived ratios
r(C0)1.000000
∠P2P1P51.000000
|P4P5|1.175571
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